ABSTRACT
Having examined the nature of the isometries on continuous function spaces, it is natural to turn to the Lp-spaces. If ϕ is a homeomorphism of [0, 1] onto itself, the simple composition operator Tf(t) = f(ϕ(t)) is not necessarily an isometry on Lp[0, 1] For example, let the function ϕ be given by
ϕ(t) =
{ t 2 , if 0 ≤ t ≤ 12 3 2 t− 1
2 , if 1
2 < t ≤ 1.
